5 accepted papers
We consider the problem of assessing a group of nodes in a network. Our focus is on vitality indices—a natural class of centrality measures that evaluate the importance of a node by examining the impact of its removal on the network. We conduct a comprehensive analysis of group vitality indices. Spe
We address the problem of selecting k representative nodes from a network, aiming to simultaneously achieve two objectives: identifying the most influential nodes and ensuring that the selection proportionally reflects the diversity within the network. We propose a general approach to accomplish thi
Edge centrality measures are functions that evaluate the importance of edges in a network. They can be used to assess the role of a backlink for the popularity of a website as well as the importance of a flight in virus spreading. Various node centralities have been translated to apply for edges, in…
In recent years, the axiomatic approach to centrality measures has attracted attention in the literature. However, most papers propose a collection of axioms dedicated to one or two considered centrality measures. In result, it is hard to capture the differences and similarities between various meas…
Vitality indices form a class of centrality measures that assess the importance of a node based on the impact its removal has on the network. To date, theoretical analysis of this class is lacking. In this paper, we show that vitality indices can be characterized using the axiom of Balanced Contribu…